Braginskii Transport Coefficients
The closed set of collisional fluid transport coefficients for a magnetized two-fluid plasma.
The Framework
Braginskii derived a systematic fluid closure for a collisional magnetized plasma by expanding the kinetic equation in the ratio of gyroradius to mean free path. The result is expressions for the viscosity, thermal conductivity, resistivity, and thermoelectric coefficients of electrons and ions, each split into components parallel to the field, perpendicular to it, and in the cross (Hall) direction.
Anisotropy
The defining feature is strong anisotropy imposed by magnetization. Parallel transport coefficients are large, set only by collisions along the field. Perpendicular coefficients are suppressed by the factor (gyrofrequency times collision time) squared, because gyration confines cross-field steps to a gyroradius. Cross coefficients, odd in the field, drive fluxes perpendicular to both the gradient and the field, including diamagnetic heat flux.
Key Coefficients
- Parallel electron heat conductivity: very large, scales as T_e^{5/2}, drives fast temperature equilibration along field lines.
- Perpendicular ion heat conductivity: sets the collisional cross-field heat loss floor before turbulence.
- Ion viscosity: a tensor with parallel, perpendicular, and gyroviscous parts governing flow damping and momentum transport.
Validity and Relevance
The Braginskii closure requires high collisionality, so the plasma is fluid-like and the distribution is near-Maxwellian. In the hot low-collisionality core it is replaced by neoclassical or kinetic theory, but it remains the standard model for the collisional edge and scrape-off layer, and for extended-MHD codes. For the Hyperion breeder concept, Braginskii coefficients inform edge and divertor modeling at the design stage; the machine is a simulation study.